DOCSLIB.ORG

Essays in Risk Management for Crude Oil Markets

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Essays in Risk Management for Crude Oil Markets Essays in Risk Management for Crude Oil Markets by Abdullah Al Mansour A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Applied Economics Waterloo, Ontario, Canada, 2012 c Abdullah Al Mansour 2012 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract This thesis consists of three essays on risk management in crude oil markets. In the first essay, the valuation of an oil sands project is studied using real options approach. Oil sands production consumes substantial amount of natural gas during extracting and upgrading. Natural gas prices are known to be stochastic and highly volatile which introduces a risk factor that needs to be taken into account. The essay studies the impact of this risk factor on the value of an oil sands project and its optimal operation. The essay takes into account the co-movement between crude oil and natural gas markets and, accordingly, proposes two models: one incorporates a long-run link between the two markets while the other has no such link. The valuation problem is solved using the Least Square Monte Carlo (LSMC) method proposed by Longstaff and Schwartz (2001) for valuing American options. The valuation results show that incorporating a long-run relationship between the two markets is a very crucial decision in the value of the project and in its optimal operation. The essay shows that ignoring this long-run relationship makes the optimal policy sensitive to the dynamics of natural gas prices. On the other hand, incorporating this long-run relationship makes the dynamics of natural gas price process have a very low impact on valuation and the optimal operating policy. In the second essay, the relationship between the slope of the futures term structure, or the forward curve, and volatility in the crude oil market is investigated using a measure of the slope based on principal component analysis (PCA). The essay begins by reviewing the main theories of the relation between spot and futures prices and considering the implication of each theory on the relation between the slope of the forward curve and volatility. The diagonal VECH model of Bollerslev et al. (1988) was used to analyze the relationship between of the forward curve slope and the variances of the spot and futures prices and the covariance between them. The results show that there is a significant iii quadratic relationship and that exploiting this relation improves the hedging performance using futures contracts. The third essay attempts to model the spot price process of crude oil using the notion of convenience yield in a regime switching framework. Unlike the existing studies, which assume the convenience yield to have either a constant value or to have a stochastic behavior with mean reversion to one equilibrium level, the model of this essay extends the Brennan and Schwartz (1985) model to allows for regime switching in the convenience yield along with the other parameters. In the essay, a closed form solution for the futures price is derived. The parameters are estimated using an extension to the Kalman filter proposed by Kim (1994). The regime switching one-factor model of this study does a reasonable job and the transitional probabilities play an important role in shaping the futures term structure implied by the model. iv Acknowledgments I offer my sincere gratitude to my supervisors, Dr. Margaret Insley and Dr. Tony Wirjanto, for their continuous support during my doctoral study. Without their time and energy they offered me, this project would have been very hard to complete. Their knowledge, experience, commitment, guidance and patience have contributed a big part of this thesis. I am also indebted to the other committee members, Dr. Dinghai Xu, Dr. Alain-Desire Nimubona and Dr. Kenneth Vetzal for their discussions and comments on my thesis Of course my deepest gratitude go to my father, Mohammad Almansour. I owe to my father something I can neither express nor repay. Thank you my father for your everlasting support and continuous encouragement. I also would like to thank my mother, Dolayyel Almansour, for the unconditional love and constant prayers which were like the light I see through. Her voice over the phone was a great source of motivation, especially when I hear her say: see you soon Abdullah. Foremost amongst the individuals to whom I am thankful is my wife, Dalal Alhammad. I owe her a grate favor that I am sure I will be still owing throughout my life. Indeed, It is a great blessing to work in such a project with such an accompany filled with inspiring love, support, patience and since of humor. I keep asking the God that whatever comes out of this success to be a source of blessing and happiness to you. I would like to thank my lovely sisters, Eman, Huda, and Lateefa for there love, concern and encouragement. Special thanks to Lateefa for taking care of my Mom. I am also thankful to my father-, mother-in-low, Hmoud Alhammad and Lolwah Alsabt, for their concern and honest prayers. Special thanks to my grandmother in-low, Umm Ali Alsabt, for her endless and honest prayers. v Many thanks to all my friends at Waterloo who made my graduate study very special and my stay in Canada feel like home. In particular, Dr. Ahmad Alojairi, Dr. Walid Bahamdan and Dr. Abdullah Basiouni. It is not the coffee we were drinking together almost every day that would keep me awake late at night, it is the honest friendship, the critical thinking and the great experience we shared that would keep me awake in my life. By the way, it's my turn! I would like to thank the department of Economics for providing the support and facilities I have needed to produce and complete my thesis. vi Dedication To my parents... See you soon. To my wife... Here you go. To my little twins... Here I am. vii Table of Contents List of Figures ix List of Tables x 1 Introductory Chapter 1 2 The Impact of Stochastic Extraction Cost on the Value of an Exhaustible Resource: the Case of the Alberta Oil Sands 8 2.1 Introduction . .8 2.2 Oil Sands Background . 11 2.3 Co-movement of Crude Oil and Natural Gas Prices . 14 2.4 Modeling the Dynamics of Natural Gas and Crude Oil Prices . 20 2.4.1 Seasonality . 24 2.4.2 Futures Pricing . 24 2.4.3 Estimation Procedure . 28 2.5 Oil Sands Valuation Model . 29 viii 2.6 Data Description for Estimation and Simulation . 32 2.7 Results . 36 2.7.1 Estimation Results . 37 2.7.2 Valuation Results . 41 2.8 Concluding Remarks . 49 3 The Relationship Between Volatility and the Forward Curve in Crude Oil Markets 51 3.1 Introduction . 51 3.2 Theoretical Background . 54 3.3 PCA Slope Measure . 61 3.4 Volatilities Model Specification . 65 3.5 Data Description . 67 3.6 Estimation Methodology . 73 3.7 Estimation Results . 75 3.8 Application: Minimum Variance Hedge Ratio . 79 3.9 Concluding Remarks . 82 4 Contango and Backwardation in the Crude Oil Market: A Regime Switch- ing Approach 84 4.1 Introduction . 84 4.2 Convenience Yield in Commodities Price Modeling . 87 ix 4.3 Regime Switching Model Specification . 89 4.4 Futures Pricing . 95 4.5 Estimation Methodology . 96 4.6 Data Description . 101 4.7 Estimation Results . 104 4.7.1 Model Comparison . 111 4.7.2 The Impact of the Transitional Probabilities . 112 4.8 Concluding Remarks . 117 5 Conclusion 119 Bibliography 123 APPENDICES 132 A Appendix to Chapter 4 133 A.1 The Definition of the Q Measure . 133 A.2 Xt in the Q Measure . 134 A.3 Futures Price Formula Derivation . 135 A.4 Hamilton (1994) Filtration Procedure . 136 x List of Figures 2.1 WTI Crude Oil and HH Natural Gas Prices . 14 2.2 Crude Oil and Natural Gas Correlation . 16 2.3 Crude Oil and Natural Gas Correlation Term Structure . 20 2.4 Example of Natural Gas Forward Curve . 34 2.5 Implied Forward Curves . 40 2.6 Oil Sand Project Value . 42 2.7 The Impact of N. Gas Long Term Component Volatility . 43 2.8 Project Value as a Function of N. Gas Long Term component . 45 2.9 Impact of N. Gas Process on the Switching Prices Under Model I : Backwar- dation Case . 46 2.10 Impact of N. Gas Process on the Switching Prices Under Model II : Back- wardation Case . 47 2.11 Impact of N. Gas Process on the Switching Prices Under Model I : Contango Case....................................... 48 2.12 Impact of N. Gas Process on the Switching Prices Under Model II : Contango Case....................................... 50 xi 3.1 WTI Crude Oil Forward Curve at Different Points in Time . 52 3.2 PCA Loadings of the Futures Price Returns . 63 3.3 Loadings of the 1st PC of the Centered Futures Prices . 64 3.4 Time Series of the Relative Slope Factor It .................. 65 3.5 Time Series of the Slope Factor, It, and the Actual Spot Returns Volatility, σa ........................................ 71 3.6 Scatter Plot of the Slope Factor, It, and the Actual Spot Returns Volatility, σa ........................................ 72 3.7 Time Series of The Hedging Portfolio Return . 82 4.1 The Implied Forward Curve of Gibson and Schwartz (1990) Model . 90 4.2 Crude Oil Price and Return Series .
Load more

Recommended publications
  • Term Structure Models of Commodity Prices
    TERM STRUCTURE MODELS OF COMMODITY PRICES Cahier de recherche du Cereg n°2003–9 Delphine LAUTIER ABSTRACT. This review article describes the main contributions in the literature on term structure models of commodity prices. A first section is devoted to the theoretical analysis of the term structure. It confines itself primarily to the traditional theories of commodity prices and to their explanation of the relationship between spot and futures prices. The normal backwardation and storage theories are however a bit limited when the whole term structure is taken into account. As a result, there is a need for an extension of the analysis for long-term horizon, which constitutes the second point of the section. Finally, a dynamic analysis of the term structure is presented. Section two is centred on term structure models of commodity prices. The presentation shows that these models differ on the nature and the number of factors used to describe uncertainty. Four different factors are generally used: the spot price, the convenience yield, the interest rate, and the long-term price. Section three reviews the main empirical results obtained with term structure models. First of all, simulations highlight the influence of the assumptions concerning the stochastic process retained for the state variables and the number of state variables. Then, the method usually employed for the estimation of the parameters is explained. Lastly, the models’ performances, namely their ability to reproduce the term structure of commodity prices, are presented. Section four exposes the two main applications of term structure models: hedging and valuation. Section five resumes the broad trends in the literature on commodity pricing during the 1990s and early 2000s, and proposes futures directions for research.
    [Show full text]
  • EC3070 FINANCIAL DERIVATIVES GLOSSARY Ask Price the Bid Price
    EC3070 FINANCIAL DERIVATIVES GLOSSARY Ask price The bid price. Arbitrage An arbitrage is a financial strategy yielding a riskless profit and requiring no investment. It commonly amounts to the successive purchase and sale, or vice versa, of an asset at differing prices in different markets. i.e. it involves buying cheap and selling dear or selling dear and buying cheap. Bid A bid is a proposal to buy. A typical convention for vocalising a bid is “p for n”: p being the proposed unit price and n being the number of units or contracts demanded. Backwardation Backwardation describes a situation where the amount of money required for the future delivery of an item is lower than the amount required for immediate delivery. Backwardation is a signal that the item in question is in short supply. The opposite market condition to backwardation is known as contango, which is when the spot price is lower than the futures price. In fact, there is some ambiguity in the usage of the term. According to the definition above, backwardation is when Fτ|0 <S0, where Fτ|0 is the current price for a delivery at time τ and S0 is the current spot price. In an alternative definition, backwardation exists when Fτ|0 <E(Fτ|t) with 0 <t<τ, which is when the expected future price at a later date exceeds the futures price settled at time t = 0. In modern usage, this is called normal backwardation. Buyer A buyer is a long position holder who has agreed to accept the delivery of a commodity at some future date.
    [Show full text]
  • Copyrighted Material
    k Trim Size: 6in x 9in Sinclair583516 bindex.tex V1 - 05/04/2020 9:51 P.M. Page 219 INDEX Bid-ask spreads (total cost component), 200 A Bitcoin, 172–173, 172f Acceleration, 60 Black-Scholes-Merton (BSM) Adjustment repair, 86 assumptions/equation/model, 2–4, 6, Alpha decay, 15–16 Anchoring, 19 108, 113, 115, 183, 192 Arbitrage counterparty risk, 178–179 Black-Scholes-Merton (BSM) PDE, 5, 116 Arbitrage pricing theory (APT), 63 Bonds, 49–50 Bonferroni’s correction, usage, 23 k ASPX option profits, taxation, 187 219 k Asymmetric implied volatility skew, 191 Broken wing butterflies/condors, 99–100 ATM, 104, 106t, 123, 131t, 137 Butterflies, 95–100, 96f, 98t At-the-money covered call, delta level, 135 BXMD/BXM/BXY, 133, 134t Autocorrelation, 73f, 91 Availability heuristic, 19 C Average return, calculation, 24 Calendar spread, 100–102 Calls, 55f, 129–136, 129f, 132f, 142 B call spread, 130f, 131t, 142f, 143t Back-tested rules, performer sample, 23 implied volatility, level (example), 140t Backwardation, 61, 62 put-call parity/relationship, 95, 115, 116 Badly priced butterfly, returns (summary strike call, 118f, 120f statistics), 98t Capital asset pricing model (CAPM), Badly priced condor, returns (summary development, 63 statistics), 98t Cash flows, taxation rate, 6 Bankruptcy, risk (increase),COPYRIGHTED66 Catastrophe MATERIAL theory, 20 Bayesian model, usage, 30 Chicago Board Options Exchange (CBOE), 16, Behavioral biases, inefficiency, 67–68 36, 45–46, 133, 134f Behavioral finance, 16–21 CNDR index, 45, 45f Best, defining (possibility), 121 Commissions (total cost component), 200 Beta, 67–68, 68t, 82, 196 Commodities, 47–49, 48t, 49t BFLY index, 45, 46f Condors, 95–100, 96f, 97f, 98t, 104t Biases, 18–20, 23, 30, 113 Confidence, 61–62, 71–75, 80 k k Trim Size: 6in x 9in Sinclair583516 bindex.tex V1 - 05/04/2020 9:51 P.M.
    [Show full text]
  • Momentum Strategies in Commodity Futures Markets
    EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE 393-400 promenade des Anglais 06202 Nice Cedex 3 Tel.: +33 (0)4 93 18 32 53 E-mail: [email protected] Web: www.edhec-risk.com Momentum Strategies in Commodity Futures Markets Joëlle Miffre Associate Professor of Finance, EDHEC Business School Georgios Rallis Cass Business School, Ph.D. Student ABSTRACT The article tests for the presence of short-term continuation and long-term reversal in commodity futures prices. While contrarian strategies do not work, the article identifies 13 profitable momentum strategies that generate 9.38% average return a year. A closer analysis of the constituents of the long-short portfolios reveals that the momentum strategies buy backwardated contracts and sell contangoed contracts. The correlation between the momentum returns and the returns of traditional asset classes is also found to be low, making the commodity-based relative-strength portfolios excellent candidates for inclusion in well-diversified portfolios. Keywords: Commodity futures, Momentum, Backwardation, Contango, Diversification JEL classification codes: G13, G14 Author for correspondence: Joëlle Miffre, Associate Professor of Finance, EDHEC Business School, 393 Promenade des Anglais, 06202, Nice, France, Tel: +33 (0)4 93 18 32 55, e-mail: [email protected] A version of this paper is forthcoming in the Journal of Banking and Finance. The authors would like to thank Chris Brooks and two anonymous referees for helpful comments. EDHEC is one of the top five business schools in France owing to the high quality of its academic staff (104 permanent lecturers from France and abroad) and its privileged relationship with professionals that the school has been developing since its establishment in 1906.
    [Show full text]
  • ERIC C. CHANG Office Address Shanghai Advanced Institute Of
    ERIC C. CHANG Office Address Shanghai Advanced Institute of Finance Shanghai Jiaotong University Room 610, 211 West Huaihai Road Shanghai, P.R. China, 200030 Tel: 86-21-6293-2129 E-mail: [email protected] EDUCATION 1982 Ph.D. in Finance (Major) and in Statistics and Econometrics (Minor) Purdue University (West Lafayette, Indiana USA) 1979 MBA in Finance Wright State University (Dayton, Ohio USA) 1974 B.S. in Civil Engineering Cheng Kung University (Taiwan) ACADEMIC APPOINTMENTS 2018 – present Professor in Finance Shanghai Advanced Institute of Finance Shanghai Jiaotong University (Shanghai, China) 2007 – 2018 Chung Hon-Dak Professor in Finance Faculty of Business and Economics The University of Hong Kong (Hong Kong) 1998 – 2018 Chair Professor of Finance (tenured) School of Business / School of Economics and Finance Faculty of Business and Economics The University of Hong Kong (Hong Kong) 1995 – 1998 Invesco Chair Professor of International Finance (tenured) The DuPree College of Management Georgia Institute of Technology (Atlanta, Georgia, USA) 2003 – 2009 Visiting Professor Executive MBA Program Fudan University (Shanghai, PRC) 2005 – 2009 Visiting Professor Executive Education Program Shenzhen Graduate School of Business Peking University (Shenzhen, PRC) 30/06/2019 Page 1 1986 – 1995 Assistant, Associate and Professor in Finance (tenured) College of Business and Administration University of Maryland (College Park, Maryland, USA) 1992 – 1994 Reader (Visiting) in Finance School of Business and Management Hong Kong University of
    [Show full text]
  • Designing and Applying a Nonparametric Option Valuation Model
    DOI: 10.5817/FAI2016-1-3 No. 1/2016 Designing and Applying a Nonparametric Option Valuation Model Jan Vlachý Czech Technical University in Prague Masaryk Institute of Advanced Studies Kolejní 2637/2a, 160 00 Praha 6 E-mail: [email protected] Abstract: This paper derives, tests and discusses a comprehensive and easy to use nonparametric option-valuation model, using a representative set of historical data on underlying asset returns jointly with an assumption of minimalistic implied information on current market trend and volatility expectations. Its testing on empirical data from Warsaw Stock Exchange trading for two distinct periods of 2014 suggests that such distribution-free models are capable of delivering useful market insights as well as applicability features, in particular wherever derivative markets are relatively new, incomplete, illiquid, or with regard to the valuation of real options. Keywords: option pricing, nonparametric simulation, inefficient markets, Warsaw Stock Exchange, WIG 20 Index JEL codes: C14, G13 Introduction Since inception of the Black-Scholes model (B-S), two distinct theoretical approaches have been predominantly used to derive the value of financial options (Black and Scholes, 1973, applied both). The first (equilibrium models), represented by e.g. Merton (1976), Cox et al. (1985), Hull and White (1987), assumes stochastic processes spanning the economy and estimates their parameters. The other (no-arbitrage models), by e.g. Cox and Ross (1976), Harrison and Kreps (1979), Rubinstein (1994), tries to calibrate to a set of market prices in complete markets. Both methods derive from the premise that all market prices are correct (in other words, markets are efficient) and therefore they cannot, by definition, allow profit opportunities.
    [Show full text]
  • Normal Backwardation’ and the Theory of Storage
    Kaldor and the relationship between ‘normal backwardation’ and the theory of storage Carlo Cristiano and Paolo Paesani 1. Introduction Standard explanations of the relationship between commodity prices at different delivery dates (e.g., Clark et al. 2001) are based on the theory of storage. The theory posits that stocks of commodities have a productive value, a convenience yield, deriving from the possibility of meeting unexpected demand while avoiding the cost of frequent revisions in production and of manufacturing disruptions and varying inversely with the level of stocks (Geman 2005). At the same time, holding stocks entails financial and storage costs (carrying costs). These costs, net of convenience yield, determine the difference between futures prices at different delivery dates through arbitrage operations. The theory of storage was developed between the 1940s and the 1960s, mainly by the US economist Holbrook Working, in alternative to the Keynes-Hicks theory of ‘normal backwardation’ (Telser 1958; Cootner 1960). The main difference between the two theories may be summarized as follows. Whereas the theory of normal backwardation posits that futures prices tend to systematically underestimate future expected prices (proxied by spot prices), as producers hedge against the risk of price declines by selling forward at a discount, the theory of storage assumes no such bias. As inventories decline (increase), their convenience yield increases (falls) and spot prices Carlo Cristiano (University of Pisa), Paolo Paesani (University of Rome, Tor Vergata). The authors are grateful to Marco Dardi, Jovanovic Franck, Cristina Marcuzzo, Annalisa Rosselli, for their comments on earlier versions of the paper. The usual disclaimer applies.
    [Show full text]
  • Futures, Forward and Option Contracts How a Futures Contract
    1 CHAPTER 34 VALUING FUTURES AND FORWARD CONTRACTS A futures contract is a contract between two parties to exchange assets or services at a specified time in the future at a price agreed upon at the time of the contract. In most conventionally traded futures contracts, one party agrees to deliver a commodity or security at some time in the future, in return for an agreement from the other party to pay an agreed upon price on delivery. The former is the seller of the futures contract, while the latter is the buyer. This chapter explores the pricing of futures contracts on a number of different assets - perishable commodities, storable commodities and financial assets - by setting up the basic arbitrage relationship between the futures contract and the underlying asset. It also examines the effects of transactions costs and trading restrictions on this relationship and on futures prices. Finally, the chapter reviews some of the evidence on the pricing of futures contracts. Futures, Forward and Option Contracts Futures, forward and option contracts are all viewed as derivative contracts because they derive their value from an underlying asset. There are however some key differences in the workings of these contracts. How a Futures Contract works There are two parties to every futures contract - the seller of the contract, who agrees to deliver the asset at the specified time in the future, and the buyer of the contract, who agrees to pay a fixed price and take delivery of the asset. 2 Figure 34.1: Cash Flows on Futures Contracts Buyer's Payoffs Futures Price Spot Price on Underlying Asset Seller's Payoffs While a futures contract may be used by a buyer or seller to hedge other positions in the same asset, price changes in the asset after the futures contract agreement is made provide gains to one party at the expense of the other.
    [Show full text]
  • The Term Structures of Oil Futures Prices
    The Term Structures of Oil Futures Prices Jacques Gabillon Oxford Institute for Energy Studies WPM 17 1991 The contents of this paper are the author’s sole responsibility. They do not necessarily represent the views of the Oxford Institute for Energy Studies or any of its Members. Copyright 0 1991 Oxford Institute for Energy Studies Registered Charity, No: 286084 All rights resewed. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the Oxford Institute for Energy Studies. This publication is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher’s prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. ISBN 0 948061 59 6 EXECUTIVE SUMMARY In recent years, there has been a massive development of derivative financial products in oil markets. The main interest came from large energy end-users who found in them a welcome opportunity to lock in fixed or maximum prices for their supplies over a period of time. Oil companies and oil traders were able to provide tailor-made swaps or options for the specific needs of the end-users. It all started with refined petroleum product swaps traded only for short maturities. Soon after, a new interest in long-term swaps and options on crude oil emerged.
    [Show full text]
  • Valuing Financial Futures with a Stochastic, Endogenous Index-Rate Covariance
    Valuing Financial Futures with a Stochastic, Endogenous Index-Rate Covariance Philippe Raimbourg* Paul Zimmermann† July 25, 2018 Abstract Revisiting the two-factor valuation of financial futures contracts and their derivatives, we propose a new approach in which the covariance process between the underlying asset price and the money market interest rate is set endogenously according to investors’ arbitrage opera- tions. The asset-rate covariance turns out to be stochastic, thereby explicitly capturing futures contracts’ marking-to-market feature. Our numerical simulations show significant deviations from the traditional cost-of-carry model of futures prices, in line with Cox, Ingersoll and Ross’s (1981) theory and a large corpus of past empirical research. Our empirical tests show a hitherto undocumented impact of several index points magnitude from the recent U.S. Federal Reserve interest rate hikes on the S&P 500 daily spot-futures basis, highlighting the effect of monetary policy at low frequencies on the backwardation vs. contango regime, and shedding new light on Keynes’s (1930) theory of normal backwardation. JEL classification: G13, G30, G32 Keywords: Futures Contracts; Risk Premium; Normal Backwardation; Contango; Stochastic Covariance; Endogenous Covariance. *University Paris 1 Pantheon-Sorbonne,´ Paris. Email: [email protected]. †IESEG´ School of Management, Department of Finance, Paris. Email: [email protected]. The authors thank Jean-Paul Laurent, Olivier Le Courtois, Franck Moraux, Nicolas Leboisne, and participants at the 2018 AFFI Conference, the 2018 IRMC Conference, the 2018 FMA European Conference, and the 2018 World Finance Confer- ence for helpful comments and suggestions. 1 Two economic explanations are usually put forward to account for the deviation observed between contemporaneous spot and futures prices, also called the spot-futures basis.
    [Show full text]
  • Introduction to Financial Mathematics Concepts and Computational Methods
    Introduction to Financial Mathematics Concepts and Computational Methods Arash Fahim Introduction to Financial Mathematics Concepts and Computational Methods Arash Fahim Florida State University July 8, 2019 Copyright © 2019, Arash Fahim This work is licensed under a Creative Commons Attribution-NonCommercial- ShareAlike 4.0 International License. You are free to: Share—copy and redistribute the material in any medium or format Adapt—remix, transform, and build upon the material Under the following terms: Attribution—You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. NonCommercial—You may not use the material for commercial purposes. ShareAlike—If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. This publication was made possible by an Alternative Textbook Grant issued by Florida State University Libraries. This work is published by Florida State University Libraries, 116 Honors Way, Tallahassee, FL 32306. DOI: 10.33009/financialmath1 ii Dedicated to Nasrin, Sevda and Idin. iv Notations v Table 1: Table of Notation A Y¨ B fi union of two disjoint set A and B Rd fi d-dimensional Euclidean space Rd Rd ` fi All points in with nonnegative coordinates x P Rd fi d-dimensional column vector minpx, yq “ fi component-wise minimum of two vectors pminpx1, y1q, ..., minpxn, ynqq x` “ minpx, 0q fi component-wise minimum of a vector with zero vector AT fi transpose of matrix A x ¨ y “ xTy fi inner (dot) product in Euclidean space A “ 0 fi all the entities of the matrix (vector) A are zero A ‰ 0 fi at least of the entities of the matrix (vector) A is nonzero A ¥ 0 (A ¡ 0) fi all the entities of the matrix (vector) A are non- negative (positive) ∇f fi column vector of gradient for a differentiable function f : Rd Ñ R ∇2f fi Hessian matrix for a twice differentiable function f : Rd Ñ R P or Pˆ fi Probability PpAq (resp.
    [Show full text]
  • Has the Performance of the Hog Options Market Changed?
    Has the Performance of the Hog Options Market Changed? Hern´an A. Urcola and Scott H. Irwin∗ June 2006 Selected Paper prepared for presentation at the American Agricultural Economics Association Annual Meeting, Long Beach, California, July 23–26, 2006 Copyright © 2006 by Hern´an A. Urcola and Scott H. Irwin. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. ∗Hern´an A. Urcola ([email protected]) is a Graduate Research Assistant for the Farmdoc Project in the Department of Agricultural and Consumer Economics at the University of Illinois at Urbana- Champaign. Scott H. Irwin is the Laurence J. Norton Professor of Agricultural Marketing in the De- partment of Agricultural and Consumer Economics at the University of Illinois at Urbana-Champaign. 1 Has the Performance of the Hog Options Market Changed? Abstract The hog option contract has served as a risk management tool for the pork industry for more than 20 years. However, very limited information exists about how this market behaves and how it was affected by the contract redesign of 1996. This paper evaluates the efficiency of hog options markets comparing its pricing function during the live hog contract period to the lean hog contract period. Trading returns are computed and adjusted for risk using the Sharpe ratio and the Capital Asset Pricing Model. When the whole sample period is analyzed, results indicate that no profits can be made by taking either side of the hog options markets. However, analyzing the live and the lean hog contracts separately, some evidence suggest that opportunities for speculative profits existed during the live hog contract period.
    [Show full text]